Abstract

We develop a three-dimensional nonlinear dynamic model in which the stock
markets of two countries are linked through the foreign exchange market. Connections are due to the trading activity of heterogeneous speculators. Using
analytical and numerical tools, we seek to explore how the coupling of the markets may affect the emergence of bull and bear market dynamics. The dimension
of the model can be reduced by restricting investors' trading activity, which enables the dynamic analysis to be performed stepwise, from low-dimensional cases
up to the full three-dimensional model. In our paper we focus mainly on the
dynamics of the one- and two- dimensional cases, with numerical experiments
and some analytical results, and also show that the main features persist in the
three-dimensional model.